Galerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensions
AffiliationUniversity of Chester
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AbstractIn this paper, we consider a two-dimensional Schodinger-type equation with a dynamical boundary condition. This model describes the long-range sound propagation in naval environments of variable rigid bottom topography. Our choice for a regular enough finite element approximation is motivated by the dynamical condition and therefore, consists of a cubic splines implicit Galerkin method in space. Furthermore, we apply a Crank-Nicolson time stepping for the evolutionary variable. We prove existence and stability of the semidiscrete and fully discrete solution.
CitationAntonopoulou, D. (2015). Galerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensions. ESAIM: M2AN - Mathematical Modelling and Numerical Analysis, (49)4, 1127-1156. DOI: 10.1051/m2an/2015004
PublisherEDP Sciences / SMAI
DescriptionThis is the author's PDF version of an article published in ESAIM: Mathematical modelling and numerical analysis© 2015. The definitive version is available at http://www.esaim-m2an.org/
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